Wavelength Calculator
The wavelength calculator solves v = fλ for wavelength, frequency or wave speed, and gives the energy of one photon for light and radio waves.
Wavelength λ
- Frequency f
- 2.4 GHz
- Wave speed v
- 2.99792 × 10⁸ m/s
- Period T = 1 ÷ f
- 4.16667 × 10⁻¹⁰ s
- Working
- λ = v ÷ f = 2.99792 × 10⁸ ÷ 2.4 × 10⁹ = 0.124914 m
- Photon energy E = hf h = 6.62607015 × 10⁻³⁴ J s and 1 eV = 1.602176634 × 10⁻¹⁹ J, both exact.
- 1.59026 × 10⁻²⁴ J = 9.9256 × 10⁻⁶ eV
How the Wavelength Calculator works
Wavelength, frequency and wave speed are tied by one formula for wavelength and frequency: v = f × λ. A wave moving at speed v that passes f crests a second has crests v ÷ f apart, so λ = v ÷ f and f = v ÷ λ.
For light, radio and every other electromagnetic wave in a vacuum, v is the speed of light, c = 299,792,458 m/s exactly. A 2.4 GHz Wi-Fi signal has a wavelength of 299,792,458 ÷ 2,400,000,000 = 0.124914 m, or 12.4914 cm.
Sound in air at 20 °C travels at about 343 m/s, so middle A at 440 Hz has a wavelength of 343 ÷ 440 = 0.779545 m, about 78 cm. Sound is a million times slower than light, so the same frequency gives a far shorter wave.
The energy of photon formula is E = h × f, or E = h × c ÷ λ, where Planck's constant h = 6.62607015 × 10⁻³⁴ J s. In electronvolts, h × c = 1,239.84 eV nm, so E in eV is 1,239.84 ÷ λ in nanometers. A 532 nm green laser has photons of 1,239.84 ÷ 532 = 2.33053 eV. The 2.4 GHz Wi-Fi photon carries 9.9256 × 10⁻⁶ eV, which is why radio waves cannot break chemical bonds while ultraviolet photons, above about 3.1 eV, can.
Wavelength Calculator FAQ
How do I convert wavelength to frequency?
Divide the wave speed by the wavelength. For light, f = 299,792,458 ÷ λ in meters: 532 nm is 0.000000532 m, so f = 5.63520 × 10¹⁴ Hz, or 563.52 THz.
Does the frequency change when light enters water?
No. The frequency stays the same and the speed drops to c ÷ n, where n is the refractive index, about 1.333 for water. The wavelength shrinks by the same factor: 532 nm light is 399 nm in water.
What is the period of a light wave?
The period is 1 ÷ f, the time between crests. Light oscillates hundreds of trillions of times a second, so one period of 532 nm light is 1.77 × 10⁻¹⁵ s, under two femtoseconds.
How do I find the frequency of a sound from its wavelength?
Divide the speed of sound by the wavelength. In air at 20 °C a 1 m sound wave is 343 ÷ 1 = 343 Hz, and a 10 cm one is 3,430 Hz.